Section A
Q1.
(a) A company produces two type of sauces - A and B. Both these sauces are made by blending two ingredients - X and Y. A certain level of flexibility is permitted in the formulae of these products. Indeed, the restrictions are that (i) B must contain no more than 75 percent of X, and (ii) A must contain no less than 25 percent of X, and no less than 50 percent of Y. Up to 400 kg of X and 300 kg of Y could be purchased. The company can sell as much of these sauces as it produces at a price of ₹ 18 for A and ₹ 17 for B. The ingredients X and Y cost ₹ 1.60 and ₹ 2.05 per kg respectively. The company wishes to maximize its net revenue from the sale of these sauces. Formulate this problem as LP model.
(a) The production department of a company requires 3600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is ₹ 36 and cost of carrying inventory is 25 percent of the investment in the inventories. The price is ₹ 10 per kg. Help the Purchase Manager to determine an ordering policy for raw material.
(b) Show that a necessary and sufficient condition for the existence of a feasible solution to the transportation problem is sum_{i=1}^{m} ai = sum_{j=1}^{n} bj. That is, the total capacity (or supply) must equal requirement (or demand).
(c)
Solve the following game after reducing it to a 2 × 2 game. Player B | | B1 | B2 | B3 |
|-------|-------|-------|-------|
| A1 | 1 | 7 | 2 |
| A2 | 6 | 2 | 7 |
| A3 | 5 | 1 | 6 |
